9. Explain using the divisibility rules

Is the product of two consecutive integers always multiple of \(2\)? Why? What about the product of three consecutive integers? Is it always a multiple of \(6\)? Why or why not? What can you say about the product of \(4\) consecutive integers? What about the product of five consecutive integers?

 

Ans:

 

(1) Two consecutive integers:

 

Answer: Yes, the product of two consecutive integers always multiple of 2.No, the product of two consecutive integers not always multiple of 2.

 

Reason: One of two consecutive integers is always divisible by 3.Both numbers are always odd.Both consecutive integers are always even.One of two consecutive integers is always even.

 

(2) Three consecutive integers:

 

The product of three consecutive integers is always a multiple of .

 

Reason: Both numbers are always odd.At least one is even and one must be divisible by 3.All three factors are divisible by 3.All three factors are even.

 

(3) Four consecutive integers:

 

(4) Five consecutive integers: